What is a Math Discussion?

What is a Math Discussion? A Definition to Work From…

Often we talk about teaching practices assuming we all know what each other is talking about. However, we come from different schools and experiences, and our definitions are often different. So, I ask… What is a math discussion?

What is a math discussion in your classroom?
What is a math discussion in your school?
What is a math discussion in your state?

Luckily for us, NCTM, National Council for Teachers of Mathematics, has written a book Principles to Actions that gives us a common, clear definition which answer that question what is a math discussion?

“a purposeful exchange of ideas through classroom discussion. Opportunities to share ideas and clarify understandings, construct convincing arguments regarding why and how things work, develop a language for expressing mathematical ideas, and learn to see things from other perspectives.”

NCTM, Principles to Actions

So, let’s work through this meaty definition together and break it down, shall we?

Purposeful. 

Math discussions are planned for. They do not just happen. We have to spend time before the discussion to think about what we want our students to talk about. In fact, we have to know the math pretty well to facilitate a successful math discussion. 

Opportunities to share ideas

In math discussions students have to share their ideas and listen to other’s ideas. How do students share in your math discussions? I suggest you have a few students share their pathways to a solution and make it visual→ chart what they are saying, putt heir work under the document camera, have students make a chart,… something so that others can see their work and speak about their work referring directly to it as evidence in the discussion. 

Construct convincing arguments about how and why things work

This can start as early as kindergarten and continue on until high school. Students, people, of all ages can work on this skill. In fact this requires LOTS of different skills. However, students in primary grades can talk about why putting their unifix cubes in sticks of 10 made it easier for them to solve because they could count a 10 instead of saying 1,2,3,4,5,6,7,8,9,10. Students in 3rd grade can describe how the commutative property works by manipulating their array. And students in middle school can create an argument that a double number line is more effective than a ratio table for showing a relationship. These strategies work for all grade levels. 

Develop language for expressing mathematical ideas 

Language development and vocabulary are hot topics in education. We’re always wondering about how we can get students to use academic vocabulary, aren’t we? Well, there’s no better way than to use the vocabulary in context for real purposes. Math discussions allow students to use math vocabulary and language for a real purpose– describing their thinking and wondering bout others’ math ideas. 

Learn to see things from other perspectives

This is probably my favorite because this transcends the math classroom. In fact, I think THIS is how math can change the world. In math we can teach our students that although their may sometimes be one answer there are often MANY right answers and EVEN MORE pathways to those answers. We can teach out students that it is okay to do things differently. That we can wonder and appreciate perspectives. That we seek to understand others’ perspectives to help us learn. Man, what a different world we will live in when this type of thinking is the norm. 

A Guided to Engaging Math Discussions

This guide can help you start to answer that question, “What is a Math Discussion?” It is completely free… made by a teacher (Me, Mona) for you! 👇🏾 Grab your copy right here!

How Can We Start Math Discussions in Our Classroom?

#1 Establish a meeting place. I personally like a circle for a math discussion. It allows students to see each other. There is really something special about circles. Everyone is fully seen, unobstructed and occupies the same about of space as their peer. (LINK)

#2 Start with a notice and wonder. Have your students notice and wonder about the work you made visual. This simple structure allows all of your students to engage. Just simply say something you see. However, because this structure is so open it allows for students to take it as deep as they are ready to go with their observations and wonderings.

#3 Use a turn and talk. Turn and talks are my method to engage every student from the very first interaction in the math discussion. Once several students have shared and we have some math ideas to discuss I ask students to turn and talk. This ensures every child has talked before anyone speaks to the whole group. I like to think of this time as a warm up for students. It’s a place to practice and rehearse your ideas before you jump into sharing them with the whole class. 

#4 Listen Closely. Make discussions success are heavily dependent on the facilitators ability to listen. When we listen closely to what students are saying with the intent to understand their thinking we are better able to help guide them toward deep mathematical understanding by asking the right questions and posing the right prompts. 

What is a Math Discussion?

Can you answer that question now? What would you tell a colleague if they asked you that question right now? I’d love to hear your definition, in your own words! Leave it in the comments below.

I talk more about how I use math discussions in my classroom on Episode 2 of Honest Math Chat & this blog post.

On episode 8 you’ll find 3 tips to Boost Participation in Math Discussions